Dependence of the subharmonic signal from contrast agent microbubbles on ambient pressure: A theoretical analysis

This paper investigates the dependence of the subharmonic response in a signal scattered by contrast agent microbubbles on ambient pressure to provide quantitative estimations of local blood pressure. The problem is formulated by assuming a gas bubble encapsulated by a shell of finite thickness with dynamic behavior modeled by a nonlinear viscoelastic constitutive equation. For ambient overpressure compatible with the clinical range, the acoustic pressure intervals where the subharmonic signal may be detected (above the threshold for the onset and below the limit value for the first chaotic transition) are determined. The analysis shows that as the overpressure is increased, all harmonic components are displaced to higher frequencies. This displacement is significant for the subharmonic of order 1/2 and explains the increase or decrease in the subharmonic amplitude with ambient pressure described in previous works. Thus, some questions related to the monotonic dependence of the subharmonic amplitude on ambient pressure are clarified. For different acoustic pressures, quantitative conditions for determining the intervals where the subharmonic amplitude is a monotonic or non-monotonic function of the ambient pressure are provided. Finally, the influence of the ambient pressure on the subharmonic resonance frequency is analyzed.